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PS - Integers mean, median

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Tue Dec 13, 2011 7:02 pm

The average of three positive integers is 44 and the median is 42. What is the least possible value of the greatest of the three numbers?

A) 6
B) 42
C) 48
D) 89
E) 128

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Source: Beat The GMAT — Problem Solving | Tue Dec 13, 2011 7:02 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Dec 13, 2011 7:45 pm

karthikpandian19 wrote:The average of three positive integers is 44 and the median is 42. What is the least possible value of the greatest of the three numbers?

A) 6
B) 42
C) 48
D) 89
E) 128

Let the three integers in increasing order be x, y, and z. Then we have to find the least possible value of z.
Then, (x + y + z)/3 = 44
Median is 42 implies y = 42
x + 42 + z = 132
x + z = 90
For z to have the smallest possible value, x should have the greatest possible value.
Now median is 42, so maximum value of x = 42
Hence, z = 90 - 42 = 48

The correct answer is C.

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MakeUrTimeCount: Master | Next Rank: 500 Posts; Posts: 104; Joined: Sun Dec 11, 2011 1:25 pmFollowed by: 3 members; Thanked: 11 times

by MakeUrTimeCount » Wed Dec 14, 2011 3:04 am

As median is 42 so sequence should be x,42,y
As Mean is 44 so here :
where x <= 42 < y

Minimum number greater than 42 in options is 48.
Ans : C

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ranvijay87: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Mon Oct 26, 2009 11:06 am; Location: Chandigarh,India

by ranvijay87 » Wed Dec 14, 2011 11:24 pm

i get x + z = 90
but if x is the greatest no
we can assume z =1
=> z = 89.
Plz explain.

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Thu Dec 15, 2011 12:36 am

@ranvijay87

The question asks for "What is the least possible value of the greatest of the three numbers"
The answer that you had mentioned is "what is the Greatest of the numbers"

The least possible value for the greatest number.....is...now you can refer the answer

ranvijay87 wrote:i get x + z = 90
but if x is the greatest no
we can assume z =1
=> z = 89.
Plz explain.

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